Scalar-metric quantum cosmology with Chaplygin gas and perfect fluid

In this paper we consider the flat FRW cosmology with a scalar field coupled with the metric along with generalized Chaplygin gas and perfect fluid comprising the matter sector. We use the Schutz's formalism to deal with the generalized Chaplygin gas sector. The full theory is then quantized canonically using the Wheeler-DeWitt Hamiltonian formalism. We then solve the WD equation with appropriate boundary conditions. Then by defining a proper completeness relation for the self-adjointness of the WD equation we arrive at the wave packet for the universe. It is observed that the peak in the probability density gets affected due to both fluids in the matter sector, namely, the Chaplygin gas and perfect fluid.Comment: 8 pages Late

Twisted Galilean symmetry and the Pauli principle at low energies

We show the twisted Galilean invariance of the noncommutative parameter, even in presence of space-time noncommutativity. We then obtain the deformed algebra of the Schr\"odinger field in configuration and momentum space by studying the action of the twisted Galilean group on the non-relativistic limit of the Klein-Gordon field. Using this deformed algebra we compute the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. It is concluded that any possible effect is probably well beyond detection at current energies.Comment: 16 pages Latex, 2 figures Some modifications made in the abstract, introduction, typographical errors correcte

Dual families of non-commutative quantum systems

We demonstrate how a one parameter family of interacting non-commuting Hamiltonians, which are physically equivalent, can be constructed in non-commutative quantum mechanics. This construction is carried out exactly (to all orders in the non-commutative parameter) and analytically in two dimensions for a free particle and a harmonic oscillator moving in a constant magnetic field. We discuss the significance of the Seiberg-Witten map in this context. It is shown for the harmonic oscillator potential that an approximate duality, valid in the low energy sector, can be constructed between the interacting commutative and a non-interacting non-commutative Hamiltonian. This approximation holds to order 1/B and is therefore valid in the case of strong magnetic fields and weak Landau-level mixing.Comment: 11 pages, no figure

Central Bank Intervention in Foreign Exchange Market under Managed Float: A Three Regime Threshold VAR Analysis of Indian Rupee-US Dollar Exchange Rate

We try to comprehensively analyze the nuances of Central Bank’s intervention in the foreign exchange market under a managed float exchange rate regime. We employ a three regime threshold VAR model and identify two endogenously determined threshold values of exchange rate cycle beyond which the Reserve Bank of India (RBI) intervenes in the Indian Rupee–US Dollar (Re/$) exchange rate market. We find that, as FIIs flow in, RBI’s interventions, mainly through open market operations, are successful in bringing the Re/$ exchange rate within the desired band. Within the band, the RBI tries only to mitigate domestic inflationary conditions

Central Bank Intervention in Foreign Exchange Market under Managed Float: A Three Regime Threshold VAR Analysis of Indian Rupee-US Dollar Exchange Rate

We try to comprehensively analyze the nuances of Central Bank’s intervention in the foreign exchange market under a managed float exchange rate regime. We employ a three regime threshold VAR model and identify two endogenously determined threshold values of exchange rate cycle beyond which the Reserve Bank of India (RBI) intervenes in the Indian Rupee–US Dollar (Re/$) exchange rate market. We find that, as FIIs flow in, RBI’s interventions, mainly through open market operations, are successful in bringing the Re/$ exchange rate within the desired band. Within the band, the RBI tries only to mitigate domestic inflationary conditions

Lorentzian path integral in Kantowski-Sachs anisotropic cosmology

Motivated by the recent development in quantum cosmology, we revisit the anisotropic Kantowski-Sachs model in the light of a Lorentzian path integral formalism. Studies so far have considered the Euclidean method where the choice of the lapse integration contour is constrained by certain physical considerations rather than mathematical justification. In this paper, we have studied the Hartle-Hawking no-boundary proposal along with the use of Picard-Lefschetz theory in performing the lapse integration. In an isotropic limit, we show our results agree with the studies made in FLRW cosmology. We also observe that in the large scale structure the no-boundary proposal tends towards a conical singularity at the beginning of time. We have also performed a massless scalar perturbation analysis with no back reaction. This reveals that if there were any perturbation present at the beginning of the universe then that would flare up at the final boundary.Comment: 9 pages, 4 figure